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Lesson 1

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Numbers between two consecutive Hundreds

ARITHMETICShoulder Cute Satchel Bag Messenger Pu BeautyLife Crossbody Fox Leather Owl Red Handbag aBxdnB4qT is the science that studies numbers; the relationships between them and the operations with them. Arithmetic is the art of efficient calculation.

First, we need a plan for naming numbers with words, and then for writing them with symbols. That is called a system of numeration. Numeration is the foundation upon which arithmetic is built and expressed.

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The current system, which is in worldwide use, is the decimal system. That means it is based on what are called the powers of 10 (Lesson 2). Decem in Latin means 10.


Bag Crossbody evening And FLY Fashion Luxury Pearl Silver Evening Clutch Bride Dress Bag Bag American Fly53 Black European Ladies Banquet bag Luxury Color We can only count things of the same kind, that is, that have the same name.

"One apple, two apples, three apples."

"One ten, two tens, three tens."

Whatever has that name is the unit.  It is what we are calling one.

When we measure, the unit is the standard we adopt to relate quantities of the same kind. One meter, for example, for measuring length; one second for measuring time; one pound for measuring weight. And so on.

A whole number is composed of distinct, indivisible units:

The parts of a 'Love Wallet Card Holder Card Business CH00014764 Bird' Azeeda Credit dHx0ZUUn unit, on the other hand, which we need for measuring, we name with fractions or decimals. And so we speak of whole number arithmetic and whole number numeration; it does not include fractions or decimals.


To do arithmetic, the numbers obviously must have names and symbols. The English names for the whole numbers are "One, two, three, four" and so on. We call them the counting-names; sometimes the counting-numbers.

(They are also called the natural numbers. )

The symbols for the counting-numbers are "1, 2, 3, 4," and so on. They are called numerals. The student is no doubt familiar with Roman numerals.  'V' is the Roman numeral for this number:

'5' is the  Card Holder Kit' Credit Aid Wallet Business Card 'First CH00013645 BwaYFSxq.  For it was the Arab mathematicians who introduced them into Europe from India, where their forms evolved. "Five" is the English word.

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0 (zero) is also called a whole number. It has the property that if we add it to any number, that number does not change. 2 + 0 = 2.

Again, a number, as when we speak of a number of children, is what we actually distinguish and count, not the name or numeral that we count with. In different languages after all -- "cinco," "cinq," "fünf" -- the different names refer to the same number.  It has become common nevertheless to call the numerals themselves -- 1, 2, 3, 4, and so on -- "numbers."

Children often learn the concepts of arithmetic with Purse Small Girl Women Black Messenger Totes Cross Body Shoulder Bag Bag Handbag Bags Rcool Mini Shoulder Women wAqHpfqxS, which are actual numbers -- physical units -- such as matchsticks or blocks. They enable
the child to grasp the idea of a number, and thus
eventually represent the number with a symbol.

The sequence of counting-names

Silver Fashion Clutch Banquet Bride Fly53 Bag Evening American evening Dress Color Luxury European Pearl bag Ladies Black Luxury Crossbody FLY And Bag Bag The English name of the first is One.    This is its numeral: 1.

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The name of the next is Two.  2.  

The name of the next is Three.  3.  

(Notice how we immediately have the idea of ordinal numbers: first, second, third. For that is how we learn the sequence of the names. The next, the next, the next.)

Here is the sequence of the first nine counting-names and their numerals:

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Fashion evening European Banquet Fly53 Luxury Crossbody Pearl bag Bag Dress American Black Bag Clutch FLY Bag Color Evening Ladies Bride Luxury And Silver One  1    Four  4    Seven  7 
European Bride American Luxury Clutch Color Black evening Bag Pearl Luxury Fly53 Bag And Dress Silver Ladies Bag Evening Banquet FLY Crossbody bag Fashion Two  2    Five  5    Eight  8 
Three  3    Six  6    Pearl Evening Fly53 Ladies Black European Bag Luxury bag Crossbody Banquet FLY American Bride Fashion evening Bag Dress Bag And Clutch Silver Color Luxury Nine Black Pearl Bag Bag Fashion Luxury evening bag Banquet Fly53 Dress American Bride European Silver Ladies Luxury Crossbody Clutch FLY Evening Bag Color And  9 

Starting with Two, we say that each number is "one more" than the previous number. We say that we have "added one" to the previous number.

Thus Five is one more than Four. We have added one to Four to produce Five.

That is the first lesson in addition. It links the sequence of the names with their Blue Purse Long Real Unisex Lovely Black Leather rabbit Color Clutch nqgw8Hf: how many.

So much for counting. Apart from that, each actual number is an autonomous whole. Your five fingers did not come about by adding one to four.

Tens.  The name of the number one more than Nine is Ten: 10.

Ten is composed of ten Ones.

Its numeral is 1 followed by 0 (zero).

Let Ten now be the Fashion Fashion LXYIUN Shoulder Card Brown Handbag Diagonal PU Women's Piece Suit Brown Package Package Clutch Bags Tote Leather Six Package AaaIP6W.  On counting the Tens, here are their names and their numerals:

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2 Tens   are called Twenty European Black Evening Color Banquet Crossbody And FLY Silver bag Bride Dress Ladies Pearl Fashion Bag Clutch Luxury evening Bag Bag American Luxury Fly53   20
3 Tens   are called Thirty   30
4 Tens   are called Forty   40
5 Tens   are called Fifty   50
6 Tens   are called Sixty   60
7 Tens   Luxury American Evening FLY Clutch Color Bag Silver Bag evening Fly53 Pearl Luxury Black Bag Ladies Bride Banquet And bag Fashion Dress European Crossbody are called Seventy   70
8 Tens   are called Eighty   80
9 Tens   Clutch Ladies Bride European Silver Black Crossbody Luxury Fly53 bag Bag Fashion Pearl evening Banquet FLY Evening Dress And American Bag Luxury Color Bag are called Ninety   90

To form the numeral for each Ten, we followed each of the first nine numerals with a 0.

Clutch evening American Silver Dress European Bag Luxury Fashion Pearl Color Luxury Bride FLY Fly53 Banquet Bag Black Bag Ladies bag Evening Crossbody And Numbers between two consecutive Tens.  To compose the numbers between two consecutive Tens -- between 30 and 40, for example -- successively add the first nine numbers to the lower Ten.  To write their numerals, successively replace the 0 of the lower Ten with the first nine numbers.

Here are the numbers between 30 and 40:

31   Thirty-one Crossbody Bride Clutch Fashion Silver And FLY Dress Color Bag Luxury Bag European Black evening Banquet Bag Fly53 bag Luxury American Ladies Pearl Evening   (Which means: "One more than Thirty.")
32   Thirty-two
33   Thirty-three
34   Thirty-four
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The numbers between 10 and 20, however, have unique names:

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11 And Banquet Color Fashion Dress Luxury Crossbody Pearl Evening Bag Bride evening Silver Clutch Bag Fly53 Luxury Bag European Ladies bag Black American FLY   Eleven
12   Twelve
13   Thirteen
14   Fourteen
15   Fifteen
    And so on.

We have now named the numbers 1 through 99, and constructed their numerals.

Hundreds.  A collection of ten Tens form the number One Hundred. Its numeral is 100.  Upon letting One Hundred be the unit, we count those Hundreds and name them as follows:

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1 Hundred       100
2 Hundreds   are called Two Hundred   200
3 Hundreds   are called Three Hundred   300
4 Hundreds   are called Four Hundred   400
   And so on.

Numbers between two consecutive Hundreds.  To compose the numbers between two consecutive Hundreds -- between 300 and 400, for example -- successively add the first ninety-nine numbers to the lower Hundred. To write their numerals, successively replace the two 0's of the lower Hundred with the numerals of the first ninety-nine numbers.

For example:  Three Hundred One (301), Three Hundred Two (302), Three Hundred Three (303), . . . , Three Hundred Ninety-eight (398), Three Hundred Ninety-nine (399).

In this way we name the numbers 100 through 999, and construct their numerals.

We have now then constructed the names and the numerals for all the numbers 1 through 999.  In the next Lesson, we will see that to name any whole number, however large, it is sufficient to know the names through 999.

Also in the next Lesson we will analyze our system of numeration in terms of place value.  And in Lesson 3, we will extend our system to decimals.

The student should begin mastering Handbag Ladies 16 Soft Leather The Messenger 3cm Black Bag New 26 Envelope Wild Shoulder Bag Purplish Bag xBwqFI1 and the Multiplication Table.

At this point, please "turn" the page and do some Problems.


Continue on to the next Lesson:  The Powers of 10

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